multiplying decimals

Multiplying decimals

To mulitply two numbers which include decimals, you should treat them as if they were whole numbers (integers) and then fix the size afterwards.
Example: work out 0.03 x 0.6

• start with 3 x 6 = 18...
• but is our answer 18 or 1.8 or 0.18 or something else?
• we can answer using decimals and place value:
  • 0.03 is 3 x 0.01 and 0.6 is 6 x 0.1
  • so 0.03 x 0.6 = 3 x 0.01 x 6 x 0.1
  • rearrange these terms to get 3 x 6 x 0.01 x 0.1 = 18 x 0.001
  • so 0.03 x 0.6 = 0.018.
    
    
• or we can answer using our understanding of fractions:
  • 0.03 x 0.6 = 3/100 x 6/10
  • so 3/100 x 6/10 = (3 x 6)/(100 x 10)
  • so 0.03 x 0.6 = 18/1000 = 0.018
    
    
• Either way, it was something else: 0.03 x 0.6 = 0.018

While it's important to understand why this works, it takes too long, so we need a short cut.
You're still going to need to multiply as if they are whole numbers. Now for the short cut:

• you can easily fix the size by ensuring that the number of digits that follow (both) decimal points in the question is the same as the number of digits after the decimal point in the answer.
• example: 0.03 x 0.6 becomes 18 in our heads, then since three digits follow the decimal point in 0 . 03 x 0 . 6 there should be the same number of digits after the decimal point in the answer. So thinking about 18, put it so that the 8 is the third digit after the decimal point: 0. 018

Need more help understanding this? Try the explanation of multiplying decimals at mymaths. Don't forget to log into your school account first.

Some questions about decimals on this page.
Practice with these multiplying decimals flashcards:

multiplying decimals flashcards